AIMR Math Group Seminar #3

FY2018

Title: Gapped-gapless correspondence for systems with codimension-one or -two boundaries

Abstract：

In condensed matter physics, topologically protected (codimension-one) edge states are known to appear on the surface of some insulators reflecting some topology of its bulk. This correspondence is called the bulk-edge correspondence and was first proved by Y.~Hatsugai. In this talk, we first revisit the bulk-edge correspondence from the point of view of K-theory and index theory. We then study three-dimensional systems with codimension-two corners/hinges and show that topologically protected corner/hinge states appear reflecting some topology of the gapped bulk and two edges/surfaces. If time permits, I will introduce an explicit example as a ``product’’ of two well-known topological phases (2d type A and 1d type AIII topological phases).